The Birthday Paradox

[Illuminati]

I found this article very interesting and thought you math guys would really enjoy it.

 

It relates to the probability of two people out of 40 having the same birthday in a room of people who's birthdays are sequential. Surprisingly enough, it's not 11%, but in fact it's 90%.

 

http://www.damninteresting.com/?p=402#more-402

 

That'll probably explain it better than I can.

[JustStuit]

Oops ;-)

 

It's not math - it's him.

 

:edit: This site doesn't seem too respectable either.

[starbug1]

Well first of all he says that people would assume 366 people would make a 100% chance two share a birthday. This is definitly not true.

 

 

If 366 people are in a room they represent every day of the year +1 extra person. So there is one person that has to fit in to a day that's already been filled. This means that at least two people share the same birthday. It has to work this way. And it is a 100% probability, therefore. However, everyone in the room, speaking in random probability, does not have to have a birthday on every day of the year. Yet if they don't, then the birthday's start piling up on each other. There may not be someone with a birthday on July 8, July 9, and July 10, but then there has to be, naturally, four people who have a birthday on July 11, or some other day, for example. The guy is stating that there is a 100% probability that two people have a birthday on the same day, which is undeniably true.

 

 

The paradox is that at 57 people, the probability raises to above 99%, which defies natural-intuition and reasoning, therefore, and that's why it's a paradox. The math was a bit confusing, but its there, and had withstood all the tests, so you have to assume its bona fide.

 

It's not math - it's him.

 

Read it again, I'm pretty certain he knows what he's talking about.

[JustStuit]

If 366 people are in a room they represent every day of the year +1. This means that at least two people share the same birthday. It has to work this way. And it is a 100% probability. However' date=' everyone in the room, speaking in random probability, does not have to have a birthday on every day of the year. Yet if they don't, then the birthday's start piling up on each other. There may not be someone with a birthday on July 8, July 9, and July 10, but there are four people who have a birthday on July 11. The guy is stating that there is a 100% probability that two people have a birthday on the same day, which is true.

 

 

The paradox is that at 57 people, the probability raises to above 99%, which defying natural-intuition, therefore, and that's why, it's a paradox. The math was a bit confusing, but its there, and it withstanding all the tests, so you have to assume its bona fide.

 

 

 

Read it again, I'm pretty certain he knows what he's talking about.[/quote']

Oops. Wow...I jumped ahead of myself. Is he doing the math right?

[starbug1]

:edit: This site doesn't seem too respectable either.

 

While the name' date=' [i']damn interesting[/i] may lead you to believe that, the stuff, at least Alan Bellows, is pretty well-researched. There is also comments on his articles, so you have some feedback.

 

Is he doing the math right?

 

This I don't know, numbers are enormous.

[JustStuit]

What equations do you use to do the math on that?

[matt grime]

It's only a paradox because you think it is unlikely, when it isn't. If there were 183 or more people in the room then the probability that there are two people with consecutuve birthdays is 1.

 

If you have 23 people in a room then there is a common birthday with probability greater than 1/2.

[starbug1]

What equations do you use to do the math on that?

 

 

Wikipedia tries to explain it through the birthday attack.

 

The math is expounded on here:

http://mathworld.wolfram.com/BirthdayProblem.html

 

Both of these sites were listed as external links on Damn Interesting